The explanation is a bit counter-intuitive. Usually mixing two solutions tend to have a positive entropy of mixing, i.e. to increase the total entropy. The result can be rationalized within of the intuitive picture of entropy as a measure of "disorder," as seen in this common visualization of the entropy of mixing, going from two separate reservoirs to a mixture. This common picture works well for fluids composed of non-interacting spheres (an idealization called ideal solutions), which works well for say mixtures of noble gases. However, the situation is more complex for solutions made up of molecules which are well defined and have strong interactions either with other molecules of the same type or with molecules with the other types of molecules making up the solution/mixture.

The case of oil/water mixtures is strikingly different qualitatively from the behavior expected of ideal solutions. The key reason is that water molecules, far from being non-interacting, in fact form rather strong bonds with each other called hydrogen bonds as shown here, due to the strong dipole moment that they have, which puts a partial negative charge on the oxygen atom and a partial positive charge on the hydrogen atoms. This effect actually causes liquid water to be surprisingly structured because the directionality of the interaction between water molecules causes them to form a loose hydrogen bonded network where the molecules have a preferential orientation as shown in the diagram above.

When oil (a solution hydrophobic molecules) is added to water, the oil molecules will disrupt this network of water molecules. The reason is that water interacts much less weakly with hydrophobic molecules than it does with itself (hence the name), which will cause water molecules to arrange themselves in a particular way (called a salvation shell) around the oil particles in order to enhance their favorable interactions with one another. This in turn causes the water to be even more structured than it originally was, because while in the bulk it can form a loose 3D network, the boundary conditions imposed by the oil-water barrier force the surrounding water molecules in a much better defined configuration. This increase in the order of water molecules in the salvation sphere compared to "free" (bulk) water molecules is the phenomenological explanation for the thermodynamic driving force of phase separation between water and oil. This effect is called the hydrophobic effect.